Question

Решите задачу, составив систему уравнений.расстояние между деревьями на реке 60 км.Это расстояние проходит моторная лодка по течению за 4 часа,а против течения за 6 часов.Найдите собственную скорость лодки и скорость течения. СРОЧНО ПОЖАЛУЙСТА ОЧЕНЬ ​

Answer 1

Problem Analysis

We are given that the distance between two trees on a river is 60 km. A motorboat takes 4 hours to travel this distance downstream and 6 hours to travel the same distance upstream. We need to find the speed of the boat and the speed of the current.

Solution

Let's assume the speed of the boat is B km/h and the speed of the current is C km/h.

When the boat is traveling downstream, its effective speed is the sum of its own speed and the speed of the current. So, the boat's effective speed downstream is B + C km/h.

When the boat is traveling upstream, its effective speed is the difference between its own speed and the speed of the current. So, the boat's effective speed upstream is B - C km/h.

We can use the formula speed = distance / time to set up two equations based on the given information:

1. When the boat is traveling downstream: - Distance = 60 km - Time = 4 hours - Speed = Distance / Time = 60 km / 4 hours = 15 km/h (equation 1)

2. When the boat is traveling upstream: - Distance = 60 km - Time = 6 hours - Speed = Distance / Time = 60 km / 6 hours = 10 km/h (equation 2)

Now, we have two equations with two variables (B and C). We can solve these equations simultaneously to find the values of B and C.

Solving the Equations

To solve the equations, we can use the method of substitution or elimination. Let's use the method of substitution.

From equation 1, we have: B + C = 15 (equation 3)

From equation 2, we have: B - C = 10 (equation 4)

We can solve equations 3 and 4 simultaneously to find the values of B and C.

Adding equations 3 and 4, we get: (B + C) + (B - C) = 15 + 10 2B = 25 B = 25 / 2 B = 12.5 km/h

Substituting the value of B into equation 3, we get: 12.5 + C = 15 C = 15 - 12.5 C = 2.5 km/h

Answer

The speed of the boat is 12.5 km/h and the speed of the current is 2.5 km/h.

Please let me know if you need any further assistance!